• entries
  • comments
  • views

About this blog

A Journal of Applied Mechanics and Mathematics by DrD

Entries in this blog


    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, #20
    © Machinery Dynamics Research, 2015

A Question of Stability


    The word stability in its several forms is widely used in nontechnical communication. A person whose life it highly consistent from day to day is said to have a stable life. When the political situation in a particular area appears to be unlikely to change, it is said to be stable. A person who is well balanced and unlikely to be easily provoked to anger is said to be a stable person. When the medical condition of a sick or injured person ceases to get worse, the person is said to be stabilized. A company on the verge of bankruptcy is said to be an unstable company. But what does the word stability mean in a technical context? Each of the foregoing examples hints at the technical meaning without really being explicit about it.



A factor g = accel of gravity was missing in the potential energy expression. That is now corrected.




Value Engineering

A toothpaste factory had a problem.  They sometimes shipped empty boxes, boxes without the tube inside. This challenged their perceived quality with the buyers and distributors. Understanding how important the relationship with them was, the CEO of the company assembled his top people. They decided to hire an external engineering company to solve their empty boxes problem. The project followed the usual process: budget and project sponsor allocated, RFP, and third-parties selected.  Six months (and $8 million) later they had a fantastic solution - on time, on budget, and high quality.  Everyone in the project was pleased.

 They solved the problem by using a high-tech precision scale that would sound a bell and flash lights whenever a toothpaste box weighed less than it should. The line would stop, someone would walk over, remove the defective box, and then press another button to re-start the line. As a result of the new package monitoring process, no empty boxes were being shipped out of the factory.

With no more customer complaints, the CEO felt the $8 million was well spent. He then reviewed the line statistics report and discovered the number of empty boxes picked up by the scale in the first week was consistent with projections, however, the next three weeks were zero! The estimated rate should have been at least a dozen boxes a day. He had the engineers check the equipment, they verified the report as accurate.

 Puzzled, the CEO traveled down to the factory, viewed the part of the line where the precision scale was installed, and observed just ahead of the new $8 million dollar solution sat a $20 desk fan blowing the empty boxes off the belt and into a bin.  He asked the line supervisor what that was about.

 "Oh, that," the supervisor replied, "Bert, the kid from maintenance, put it there because he was tired of walking over, removing the box and re-starting the line every time the bell rang.”


How to Ask for Help

How to Ask for Help

Throughout life, we all find ourselves needing to ask for help at times. Even the most rugged individualist will, at time, need help. You may need to ask a teacher for help, you may need to ask a fellow employee for help, or you may need to ask the boss for help. There are a few good ways to ask for help, and there are endless poor ways to ask. Make your request well, and there is a much better you will get the help you seek.

Since I began writing for ME Forums, I have received a great many requests for help. I am pleased to help where I can, but I am very frustrated with many of the requests. Here is such a request, typical of many that I have received:

I am engg student and need to do a project. Pls give me gud idea.

There are all sorts of problems with that request, and I want to point out some of them. It is my hope that if I tell you what works against you, you will change the way you ask.

Let us look at the small matters first, starting with spelling. Many of you seem to be very fond of abbreviations. The extensive use of abbreviations for ordinary words is simple laziness, and is offensive to the person receiving the request. Thus, while I understand what “engg” stands for in this context, it says to me, the reader, that you did not think it worth your time to spell out “engineering.” The same goes for “Pls” instead of writing out “Please.” If that is not worth your time, then it is probably not worth my time to reply to you either.

Secondly, if you would use spell check, it would tell you that “gud” is not an English word. In this case, I understand that the writer meant “good,” but sometimes I do not understand. Again, it is offensive to the reader that the writer was unwilling to even try slightly to make the request for help in proper English. These things matter.

The really big point is the third one. The writer tells nothing at all about (1) what he is interested in, (2) what the nature of his project is supposed to be, (3) what the scope of his project should be, or (4) what resources he has available to fulfill his project. Let us look at these in more detail.

Area of Interest
If I suggest a project in IC engine design to a student whose interest is mostly in wind power, it is most likely a wasted effort on my part. Why should I spend the time on something to no point at all? It does not help the student because he will not likely use the idea, and I really don’t like having my time wasted.

Nature of the Project
Is this project supposed to be a research project (design and execute an experiment to study something), or a design project (design a new gadget), or a design, build, and test project? There is a wide range of project types, and there is no point at all in getting a detailed suggestion for a project of the wrong type. Again, it wastes my time and does not help you.

Scope of the Project
Is this project supposed to be a purely pencil and paper project (nothing built, no computer work), or something more? Is it expected to include a computer simulation or FEA stress analysis? Is it expected to include a build and test phase? How much time is expected to be put into this project? A man-week, a man-month, or more? These are vastly different project scope levels, and there is no point to receiving a suggestion for a project that is too much or too little in scope.

The sort of project you can undertake depends greatly on the resources available to you. Part of this is your own mental resources (Do you really know differential equations? Are you skilled with vectors and matrices? Do you know energy methods in mechanics? Are you good at kinematics? Etc.) Another part involves the computer resources available. (Do you have CAD software? Do you have FEA/CFD software? Are they sufficient for really big problems, or are they limited student versions only?)

If your project will involve a build and test aspect, what sort of shop facilities do you have available? Do you have a CNC milling machine? Do you have a 1000 ton forming press? Do you have a precision lathe? What about testing machines? Do you have an Instron tensile testing machine? Do you have a Prony brake? Strain gages? There are all sorts of testing equipment that might be needed to carry out a project, and there is no point to beginning a project when you know that the necessary equipment is not available.

In response to the original question, “I am engg student and need to do project. Pls give me gud idea” I recently suggested that the student design, built and test a moon rocket. I said if that was too much, scale it back to simply the design. If that was too little, expand the problem to a Mars rocket instead. Now all of my answer was absurd, and I am well aware of that. But the point is, the request was absurd, so how else can it be answered?

The solution to all of the above (or at least to most of it) is engagement. You as students need to be engaged with engineering, engaged with you assignment, and engaged in thinking! The last is the most critical of all: THINKING!! Engineering is all about thinking and not in the slightest about memorizing formulas, following well written instructions, or doing what you are told. It is about thinking through your problem to a solution. Far too much of your education has been simply memorizing and regurgitating for an exam, but that has little or nothing to do with real engineering.

How does that apply? First of all, you have to think about your problem. What have you been asked to do? Are you asked for a pencil and paper study of something, are you asked for an experimental study, are you asked for a computer simulation, or just what is the end result supposed to be? When the teacher says, “Do a project” it gives you freedom to explore whatever interests you, within some range of parameters. This is more latitude than you will usually have on the job where the boss defines the problem, at least roughly. But you have to think about what sort of project you want to do, and then, if requesting help, be able to communicate that to the person you ask to help you.

You have to think your problem through to the point that you have a good idea of what resources will be required (if you are going to design a compressor, a wind tunnel will not likely be needed but other things will be needed). You need to think your problem through to the point that you have a good idea as to what is within your range of capabilities, both personal and in terms of available resources.

When it comes right down to it, you really need to invest a whole lot more effort up front, before you ask for help. You may surprise yourself; you may not need any help at all, but you have to start the process by your own thoughts. Far too many are accustomed to simply following directions, to being told what to do. It is too easy to be lazy and ask someone else to think for you. This is a recipe for failure in engineering. Get moving and THINK!

If you do have to ask for help, communicate clearly everything you know (or think you know) about the problem. Lay out your thoughts, and then ask your question in relation to the foundation you have laid. With no foundation, your request is not for help, but that someone else do your work for you.





Where Will I Find A Job??

Where Will I Find A Job??

As I read over the questions that readers post here on ME Forum and elsewhere, I sense a common theme in many of them. There seems to be a wide, dare I say almost universal, concern about where those currently in college will find employment after graduation. To a degree this is entirely understandable; we all wonder what is in our future. Even so, the level of anxiety that I sense in many of your postings strikes me as extraordinarily high. Let us consider this a bit.

Most readers of ME Forum are currently enrolled in an engineering curriculum somewhere. Some are just beginning while others are nearing the end of their undergraduate education. I would like to pose a question to all of you: Why did you go to engineering school? Why did you choose what is probably one of the most difficult curricula in any college? For the sake of this article, I'm going to presume that I have heard at least some of your answers.

It is almost universal among engineering students to be looking forward to a good job, one that will provide them a comfortable living and a substantial measure of security. This is not at all unreasonable, and is in fact entirely probable. Almost all of you can expect to be well employed and in the upper echelons of society wherever you live. You will not rank as high as the well-known politicians, nor will you be the most wealthy people in the area. But you will have stable work and a comfortable income from that work.

What does it matter where you find employment? One of the themes I see in what I read is a great many people looking for "government jobs," that is, employment with some government entity. Traditionally, "government jobs" have been very stable. As long as a government employee stays out of trouble, in most situations it is impossible to remove that employee from his government job. This feature makes government work extremely attractive to the incompetent, to those who really cannot do the job well and thus rely on the fact that they can almost never be fired. Is this why you struggle with a difficult college curriculum, so that you can be employed with those that are incompetent? Do you really want to spend your working days with people far less capable than yourself? Many of them have achieved their positions without nearly the rigorous education that you are undergoing, so I ask you, are these the ones you want to have for your close associates?

Let me tell you a personal experience. After a long career that involved both academic positions and various industrial research positions (with a few years as a solo consulting engineer), at age 59 I took a position with a research laboratory run by the U.S. Navy. It is a sad fact of life that, in the USA, most people are considered unemployable after age 60, so I was nearing the end of the time when I could look for and expect to find a new position. The job was attractive because it promised an opportunity to do some well funded work in an area I was quite interested in, the area called electro-mechanics. The position would be very stable and I would be well payed.

In my first week on the job, I was given a few documents to read but nothing really to work on. I was not too surprised and expected all that to end very soon. After about three weeks in the new position with still in no work assignment, I began to be very worried. Every place I had worked previously had plenty of work to be done and anyone not given an assignment was probably being set up to be fired. I spoke with my boss about this several times, and he very casually told me not to worry about it. That really did not relieve my concern, particularly when he was so very casual about the whole matter. I tried to find things to work on, to make myself look useful and busy. In conversation with the other engineers, a few problems were suggested, and I worked on some of those. I wrote a few technical notes, primarily just to show that I wasn't simply sitting idle at my desk. Time went by, weeks turned into months, and months turned into years. When I finally retired from that position after seven years, I estimated that I had done at most 18 months of real work. The rest of the time I simply had nothing assigned for me to work on.

Had I realized in the beginning how the game was to be played, I would have spent my days doing things that were much more productive, such as working on problems that I found interesting, writing technical papers on those problems, and probably writing a few books. In the nonproductive 5 1/2 years I had, I could have done a lot of work! But I did not realize how the game was played, and I kept expecting someone to assign to me real engineering work to do.

As I got to know the other people, I found that a few of them had ongoing projects that were of interest to them, but most had nothing to do most of the time. I am convinced that this is the pattern of government employment, the so-called "government job." There were very few people who were truly happy in their work them: most were fairly miserable in fact. But they were wedded to the paycheck and the job security that went with their "government job." They even spoke of these factors as the "golden handcuffs." Most intended to stick it out for a total of 30 years or more, so that they could retire with a good pension.

Now I ask you, the reader, is your primary goal to retire with a good pension? Is this your principal objective in life? If so, why don't you simply roll over and die now?? While it is true that no one wants to retire in poverty, most of your life is long before retirement. Retirement is the end stage of life. I have been fortunate to live almost a decade since I retired, but it is not at all uncommon for men to die within a year or two after retirement. It seems that many simply lose their purpose in life when they retire. So to live your life in preparation for retirement is foolishness of the highest order!

If preparation for retirement is not to be your principal purpose, then what should be your objective? I submit to you that your objective ought to be to find meaningful, rewarding work in the service of other people. I am not suggesting that a group of mechanical engineers become social workers, but I am saying that you should see some connection between your work and the improvement of your society, the people among whom you live. If your work does nothing to help other people, what is its lasting value? The money you bring home in your paycheck will soon be spent. The time you invested to earn that money is already spent. So what are you contributing to mankind?

Rather than looking for a secure, comfy do-nothing "government job," I suggest to you that you should be adventurous, looking for new opportunities and new ways to help others. This is urgently needed everywhere, particularly in developing countries. Look for small startup companies with new ideas for new products, things that will improve life for everyone. Many of these companies will fail, but you are young, and looking for another job after two or three years with the company that fails is no disaster. It will not reflect badly on you if the company fails; that reflects upon the management of the company rather than upon the engineering staff. Look also at very traditional companies that are doing things the way they have always been done. Many of these companies need engineering help if they are to remain competitive and to survive into the future. This may provide you an opportunity to keep an entire company functioning, providing employment for many people. There are countless other ways that we may help our fellow man, but this should always be high in our list of priorities for the work we will do. It is while you are young that you can afford to be adventurous, to take some risks and try out things that later in life will simply be too risky. Look for challenges, situations that will require it to you use everything that you have learned, and also require you to continue to learn.

There is absolutely no point to your engineering education if your goal is simply to doze the next 50 or 60 years before you die. Plan to do something with your life, something useful, something meaningful. Do not look for a place to lay your head and simply sleep away your career.



The VEProject --- Shifted Levers
A Critical Assessment



    The subject of this article is the VEProject Shifted Lever video, as found at the following URL:


    The video shows a "Shifted Lever" mechanism, a device that appears to be perpetually off balance. It is presented as a perpetual motion mechanism, that is, a machine that will run forever without any energy input other than, perhaps, an initial push. This presentation comes from the VEProject, where VEProject stands for "Visual Education Project." An educational project can be presumed to be a presentation of truth, so should we accept that the author believes that this device is truly a perpetual motion device, or that he is attempting to deceive the viewer?
    As most Mechanical Engineers know, the laws of thermodynamics show that there cannot be perpetual motion. So, are the laws of thermodynamics incorrect, or are we being deceived?



Twenty One Rules for Tech Writing


One of the things that has surprised me about the readers of ME Forum is the number of folk who want to publish technical papers. When I was an undergraduate (a very, very long time ago), publishing papers was the farthest thing from my mind. I knew that publishing was a concern for some of the faculty, but it was certainly no concern of mine! To my even greater amazement, most of those desiring to write want to write in English, even though this is not their mother-tongue. I presume that this is a natural consequence of the fact that English has come to dominate the technical literature world-wide. That is a good thing for me (I only speak one language), but I would think it must be a daunting prospect for many of you. I have great respect for anyone who would undertake to write a technical paper in a foreign language; it is quite enough of a challenge in a language that I know pretty well. But perhaps it is not so much “foreign” as it is simply a “second language,” for those of you that know multiple languages. Either way, I am impressed that you would tackle this difficult undertaking at this point in your lives.

The purpose of this article is an attempt to help those of you who wish to publish, particularly technical publications. Most of what I have to say can be applied to anything you write, comments about such matters as organization, for example. Other parts of this article apply specifically to publication in technical journals, so you must use my suggestions with understand as to where they apply and where they do not.

I am organizing this article in two main parts. The first part I have labeled as Philosophy, meaning that it provides some guiding principles to be kept in mind about the way you construct your paper. The second part is labeled Mechanics and refers to details about actual construction of the paper. You will find that both of these are important. I have been reviewing papers for many years now for ASME, SAE, Journal of Mechanism and Machine Theory, and others, and I can tell you with certainty, that many papers fail on some of the most mundane items discussed here. These things matter, and if you want your paper to be accepted, you will need to pay attention to them all.


1. Have something interesting to say. There is simply no point to attempting to write a paper on an uninteresting topic, one that does not interest you, the writer, nor the reader. There are times when it is necessary to report information that is less than fascinating, but as the writer, you should seek to find what there is about this information that is interesting and/or important to the reader and point that out. You should never choose to write on a topic where you really do not know what you are talking about; it just will not work!

2. Identify your reader. In most cases, you will not know exactly who the reader is going to be, but you should have some pretty clear ideas about him nevertheless. You will be making definite assumptions about the reader (it may be helpful to go so far as to write these out), about his background and preparation for what you are going to present. Are you writing for a broad, general audience with a limited technical background, or are you writing for someone who is a specialist in the field and perhaps has even more background than you do? The assumptions you make about the reader will have a major impact on what you say and how you say it, so it is necessary to be rather definite about the capabilities of the reader.

3. Identify your publisher. When you write, you need to keep in mind who will be publishing your work. Most established publishers have very definite requirements regarding style, page layouts, footnote/endnote requirements, and a host of other matters. Many journals will publish in each issue a short section with a title like “Information for Authors,” and today this will usually lead a link for a URL where you will find pages and pages of detailed requirements. It is better by far to be aware of these requirements before you begin writing rather than having to do major re-writing simply to meet the publisher’s requirements.

4. Organize your story in a logical form. This is often not the way things came first to you, but it is necessary to make things easy for the reader. Think about the easiest possible way to explain your subject to a reader, the sequencing of information that will enable him to most easily understand the whole topic. This will help you to keep your paper concise and focused.

5. Provide any necessary background. This is often done in an Introduction where you survey related previous work so that someone not intimately acquainted with the field can still follow your work. Depending upon the nature of the publication (journal article, technical report, lab report, etc.),  a bit of basic review may be appropriate in some situations.

6. Use correct terminology. Terms such as axial, radial, height, width, length, vertical, horizontal, cylindrical, conical, spherical, etc. have rather specific universal meanings. Be sure to describe carefully the orientation of dimension, and other similar matters that are often essential for a clear understanding. Consider the four words: depth, height, width, length. What directions are associated with each? Height is usually vertical, that is aligned with the local gravity vector. The length of something is usually the longest dimension, assuming that this dimension is horizontal, but what happens if it is not horizontal? The word depth is sometimes associated with a vertical distance, such as the water depth, but it is also associated with a horizontal distance measured away from the observer. The ambiguity of these words means that they must be used with great care. Often it is necessary to say something like, “The depth of the hole, measured in the horizontal plane, is ...” or “The width is 42 mm, as shown on the drawing.”

7. Use consistent terminology throughout. If you call something a brick at the beginning, then it must be called a brick throughout. If you start off talking about the engine, do not switch to talking about the motor. The exception to this occurs when you use a common place term to introduce an idea before giving the technically correct term. Consider for example, “The longest edge of a right triangle is called the hypotenuse.” The common term in this example is “longest edge,” but the technically correct term is “hypotenuse.”

8. Use figures, but use them sparingly. Figures can add a lot of interest to your publication, as well as conveying much information in a simple, easy to understand form. But remember that they are there to inform, to carry information from you to the reader, not simply to look pretty. They take up a lot of space, so they must convey a lot of information. On the other hand, they must not be too cluttered, with text too small to read. Labels with leader lines can help in many cases.

9. Always write a conclusion. The conclusion is important to solidify in the mind of the reader what it is that he has just read. When you write your final conclusion, be sure that your text supports everything that you are concluding and that you have told the whole story.

10. Don’t make you paper too long. Most journals impose a limit of 8 pages, including figures and references, so be concise. There are exceptions, journals that allow longer papers, but the best ones generally have a firm limit. If a paper becomes too long, the reader is very likely to loose interest before finishing, in which case, you have not reached the reader with your information and he has wasted his time.


11. Be precise in the use of words. Don’t describe everything as “efficient,” when you really mean “more effective,” “faster” “less expensive,” “more aesthetic,” etc. The bigger your vocabulary is, the easier this will be. Avoid “engineer–speak,” that is, the sort of slang that engineers often use on the job, such terms as “down-force,”  “up-draft,” “bhp,” “mip,” “CG,” “cross-over,” etc. (Does everyone know that the CM and the CG are usually the same location, although not always? Giving the whole term makes clear which you mean.) If you think they are necessary, then you must define them in the text. In this same vein, for technical publications it is never acceptable to use the abbreviated form that have become popular with instant messaging, texting, Twitter, etc. I am speaking about such things as “u r” for “you are,” “b4” for “before,” and similar extreme contractions of words.

12. Number all figures, and provide a title. In so far as possible, all figures should be uniform in style. Think twice about the use of color. It looks pretty when well reproduced, but will it always do so? Multi-color figures on a black and white copier lose most of their information. For most purposes, black lines on a white background are the best idea.

13. Number all pages. This seems obvious, but evidently it is not so to everyone. This helps put the pages in order if they get shuffled, it helps a reviewer refer to specific items, and it helps a reader to locate information given in a citation.

14. Number all equations. Again, this seems obvious, but not so to everyone. Use conventional symbols wherever possible (Greek rho for mass density, W for weight, m for mass, v for velocity, etc.) For journal publication, do not show substitutions of numeric values into an equation. Instead, solve the equation in symbols and then show the final numeric result. There may be an exception when for a professional report (such as a stress analysis for a client), you may need to show the substitution.

15. Provide section and subsection heads. This helps to give structure to your paper, conveying the logic of your presentation. Also, it suggests to the reader where to look for particular information.

16. Start a new paragraph with each new idea. The basic purpose of a paragraph is to present one, and only one, idea. This is true even for summary paragraphs where the new idea is the interrelatedness of several ideas presented previously. Single sentence paragraphs are to be avoided.

17. Use spell-check. With all the word processing capability available today, almost all of it including a spell checking feature, there is absolutely no excuse for misspelled words. Now spell-check will not check the logic of your sentences, so the simple fact that spell-check did not flag anything does not mean that everything is correct. But if spell-check does flag a word, you must correct it.

18. Punctuate and capitalize correctly. Be sure to single space after a period at the end of every sentence. When using a hyphen to break a word, do not include a space. Punctuate consistently throughout, with the publisher’s rules as your main guide. Above all, be consistent. It looks terrible to see a space on one side of a hyphen and not on the other

19. Use consistent units throughout, usually SI. This would seem to be obvious, but it is not so to everyone. Most of your work should be formulated in such a way that it is units-free, that is, so that it may be used with any consistent system of units. But when you are reporting numerical results, you will have to use units (unless you use dimension-less ratios which are not entirely satisfactory).

20. Use abbreviations correctly.  If you want to use an abbreviation, such as BWR for Boiling Water Reactor, the whole thing must be spelled out the first time, with the abbreviation immediately following in parentheses. Thus, we might say, “Westinghouse provided the Boiling Water Reactor (BWR) for the installation.” Thereafter, use BWR consistently, except at the beginning of a sentence (do not start with an abbreviation).

21. Proof-read, proof-read, proof-read! Putting the words into the computer is only the beginning of writing a paper, definitely not the end. It is necessary to proof read, looking for many different potential problems. Does every sentence make sense and say what you intended for it to say? Is your explanation complete, or are there gaps in it? Is the punctuation and capitalization all correct? Have you followed the publisher’s guidelines for format, style, equation numbering, etc.? When you have read it and re-read it many times, to the point that you think it is perfect, then get someone else to proof-read it also for you. The failure to adequately proof-read is one of the most common of failings, and it reflects very badly on the author. It says that the author did not think that this article was worth making perfect, which makes the reader wonder why he should bother with it at all?

Following these rules does not assure that your paper will be accepted by one of the leading journals of the world, but failure to follow them virtually assures that your paper will fail. The whole idea of writing a paper is to communicate something to a reader, and these rules are largely about steps that you, the author, can take to facilitate that communication. If what you say is not interesting or is unclear, then there will be no communication. These rules are all about clarity and ease of communication.




As most of us know, the Internet is a fantastic resource for information. You can find information on almost any topic you can imagine by doing an Internet search on the appropriate keywords. The flip side of this capability is that you can also find mis-information on almost any topic because there is no one to monitor the Internet for correctness. Wikipedia is a classic case in point. Many of the Wikipedia articles are highly informative and very valuable. Some, however, are highly biased and incorrect.

We have such a problem here on the ME Forum with a blog titled Differences Between SI Engine and CI Engine by ibrahim1hj. This blog author has posted a large tabular comparison of these two engine types in the About section of the blog, a place where there is no ability for anyone to add a comment. This would not be a problem except that there is a serious need to comment on this information; some of it is misleading at best. I am reproducing below the table in question, and will comment on it below the table:

From ibrahim1hj ---

About this blog

Spark Ignition (SI) engine can be compared with Compression Ignition (CI) engine system in 7 aspects. Those 7 aspects are engine speed, cycle efficiency, fuel used, time of knocking, cycle operation, pressure generated and constant parameter during cycle.






Spark Ignition Engine


Compression Ignition Engine




Engine speed


SI engines are high speed engines.


CI engines are low speed engines.




Cycle efficiency


SI engines have low thermal efficiency


CI engines have high thermal efficiency.





Fuel used


Petrol is used as fuel, which has high self ignition temperature.


Diesel is used as fuel, it has low self ignition temperature.




Time of knocking


Knocking takes place at the end of combustion.


Knocking takes place at the beginning of combustion.




Cycle operation


SI engine works on otto cycle.


CI engine works on diesel cycle.




Pressure generated


Homogeneous mixture of fuel, hence high pressure is generated.


Heterogeneous mixture of fuel, hence low pressure is generated.




Constant parameter during cycle


Constant volume cycle.


Constant pressure cycle.


DrD again here.

In his first comparison item, he says that "SI engines are high speed engines," but that "CI engines are low speed engines." Well, what does that mean? What is "high speed" and what is "low speed"? Who defines these terms? (ibrahim1hj certainly does not provide a definition.) We are left to wonder what this tells us.

Actual engine speed ranges all over the place, so terms like "high" and "low" do not mean much without providing context. Many years ago, when I was actively involved in the engine industry, I worked for a company that sold many thousands of diesel engines that had a nominal speed in the range 1800 to 2000 rpm. These were 2 stroke diesels. We also sold some much larger engines (again, 2 stroke diesels) that ran at 900 rpm, which I thought of as being "slow." More recently, I have done some work with large marine diesels that run at 90 to 110 rpm. On the other hand, this past weekend, I was at an antique engine show where I saw a number of spark ignited engines that ran at 100 to 300 rpm. My SI automobile engine easily turns up around 5000 to 6000 rpm and will go higher. My truck has an SI engine that does not like to run much over 3000 rpm top speed.

Therefore the original statements in terms of "high speed" and "low speed" are just about meaningless. I have given examples of both SI and CI engines that run at speeds all over the place. I suggest that the meaningless terms "high speed" and "low speed" should not be used in an article on ME Forum, but rather give specific values if at all possible.

Regarding comparison items 6 and 7, "Pressure Generated" and "Constant Parameter during Cycle" there are some additional difficulties. Ibrahaim1hj says that, for an SI engine "high pressure is generated" but for a CI engine "low pressure is generated." While ibrahim1hj does not specify, we might reasonably presume that he is referring to peak cylinder pressure. He goes on to describe the Otto cycle (SI engine) as employing constant volume while the Diesel cycle (CI engine) is a constant pressure cycle. The cycle descriptions are correct as far as they go, but they contribute to the idea that the diesel engine cylinder pressures are lower than those for the SI engine; this is not correct.

Actual firing cylinder pressure data is hard to obtain, but there is some information available in a very old reference (F.P. Porter, "Harmonic Coefficients of Engine Torque Curves," J of Applied Mechanics, Trans ASME, March, 1943). In this paper, Porter gives P-V diagrams and torque-piston position diagrams for a wide variety of engines. Set B2 shows a maximum cylinder pressure of about 760 psi for a 4 stroke gasoline engine (this would be an SI engine). He shows several different data sets (G1, H1, J2) for two stroke diesel engines with maximum cylinder pressures of 670, 840, and 1150 psi. For a four stroke diesel engine, he shows data sets (P2 and Q2) with maximum firing pressures of 740 and 930 psi. In most cases, the maximum firing pressures for the diesel engines exceed that for the gasoline engines. Thus it would appear that the comparisons given by ibrahim1hj are exactly backwards.

It is important to be able to check the validity of what we read on the Internet, and to verify the sources. One thing that helps in this regard is the ability to comment on items posted. Comments can both expand on the information given, and can also offer correction to errors in articles. We need this capability.


What/Where to Study


I do not have the definite statistics available, but it appears to me that the majority of the readership of ME Forums is made up of students, with a much smaller number of readers at other points in their careers. By far the greatest part of these students appear to be in India, with a number in Southeast Asia and the Middle East; there are of course a few folks scattered all over the globe. It has been very interesting to me to learn about all of you, to gain an insight into your interests and concerns. I have been very surprised by a few of the things I've learned. There are two themes that stand out in my mind:

(1) there is much uncertainty about what to study, that is, what to choose for a major,
(2) where to study.

I want to offer a few comments on both of those topics in this post. Please understand that these are simply opinions, not necessarily facts. They are based upon what I think I see in the readership and in the way the world is going at large.

What to Study

Most of you are here because you have some interest in mechanical engineering. But quite a few express uncertainty about that interest. There are questions such as, "Should I switch to EE?" or "Would it be better to major in computer science?" These questions are often connected with questions and concerns about the future job market for whatever area one does choose to major in. So what can we say about such things?

It appears to me that the world economy is shifting considerably in favor of China and India. I do not think that the United States will disappear in the world economy by any means, but I do think these other two are going to become major rivals. If that is correct, the expanding economies of China and India will have a huge need for engineers and other technical people of all sorts in the years to come. It appears to me that the economies of both China and India are rapidly developing industrial economies, economies based on industrial production of goods. This would be much like the economy of the United States during the period from 1900 to about 1975. Sadly, the United States has entered a post-industrial era, also called a service economy. This does not mean that there is no industry in the US today, but it does mean that the bigger part of the economy is now based on paper shuffling, such things as banking, insurance, litigation, and fast food. The best automobiles produced in the United States today are those produced by Japanese companies such as Toyota and Honda. The machine tool industry, which was once a thriving business sector, is almost completely dead today in the US, because it has gone overseas. Almost all electronics production has moved to Southeast Asia. The production of textiles left the United States almost 100 years ago. The United States continues to have a very large agricultural industry, but that industry employs fewer people every year to produce even greater food yields. The point I hope to make here is simply that, many of you are right where you need to be to ride the crest of the rising wave of a developing industrial economy.

Many people looking at the future think very much in terms of electronic devices doing essentially everything. But I doubt that the day will ever come when we will do such things as plant crops entirely by electronics. We may use computer programs to anticipate when to plant a crop, perhaps to determine the most economically advantageous mix of crops, to help us choose fertilizers and pesticides to maximize the yield, but putting the seed in the ground and harvesting the crop will always be mechanical functions. This is simply one example but I think there are many others similar to it. There is a great future in electronics, but there is still a great future in mechanical devices as well. A growing industrial economy needs both of these and many other things as well.

Many of you seem to be concerned about the job market in the future. Will I be able to find a job as a mechanical engineer? Should I switch to computer engineering because there will be more jobs for computer engineers than there will be for mechanical engineers? These are questions that no one can really answer with full knowledge, but I can tell you a little bit. If you are really good at what you do, whether it be mechanical engineering, electrical engineering, chemical engineering, architectural engineering, etc., you will always be able to find employment. Many people look at salary surveys and say to themselves, "oh my, this year such and such a group of engineers are receiving higher salary offers that any of the others." Well, so what? When you pause to think about it, some group must always receive the highest offers, and some other group must always receive the lowest offers. That much is a mathematical certainty, but it doesn't really tell us very much.

I should add right here that if your intention is to acquire great wealth, then you should probably get out of engineering and go into business, law, or banking. That's where the big money is. Stay in engineering only if your interest is in doing something useful and meaningful with your life while earning a comfortable living. You're not likely to get rich, but I have never seen a starving engineer.

The other side of the job market concern is about the availability of jobs. We read various publications that say that X number of engineers were hired recently by Y Corporation. Depending on whether X is a large number or a small number, we think that the job market is good or that it is bad. But I would remind everyone of you that you only need, indeed can only handle, one job at a time. As long as you have a good job, one that provide satisfaction and a reasonable standard of living, there is little more you can ask for. Whether there are job advertisements for 1000 engineers or only for a few really makes no difference at all if you have a good job.

So how do you decide what to study? The answer is really rather simple. Within broad limits, you study whatever interests you. If civil engineering is really what interests you, then by all means you should study civil engineering. There will always be jobs for civil engineers. If those imaginary little things called electrons fascinate you, then you should most certainly study electrical engineering (I always enjoy teasing EEs about working with things that are not really there. I ask them how many electrons they have actually seen. I can show them a gear, a shaft, or a cam, but can they show me an electron?) There is a great future for electrical engineers. If you enjoy seeing how things move, how work gets done, how machines can make life easier for all mankind, then you should certainly become a mechanical engineer. We will always need mechanical engineers.

But there's more to this matter of "study what interests you" than simply amusing yourself. To be assured of a job, a good job, you have to be really good at your profession. There is one way, and only one way, to become really good. That is work, work, work, and then when you think you're through, work some more. During your student days, it is important that you learn everything you possibly can. You cannot possibly put in the required level of effort for the long haul if you are not studying the topic that interests you most. If you don’t know what that topic is, then you should drop out of school and only return when you have the necessary sense of direction.

Do not ask, "why do I have to learn this?" If it is presented to you as necessary course work, your response should be to dig in and learn every bit of it as thoroughly as you possibly can. You may have no idea why you need to know about this particular subject matter, but you can be pretty well assured that it would not be in the curriculum if your faculty did not think it was important. To be sure, there are a few topics that you will study and not see again for many years, but at this point in your life there is absolutely no way to predict which of those topics fall into that category. In my own case, I really did not particularly enjoy learning crystallography in the study of materials. As things have turned out, I have never needed any of that information about crystallography. But I had no way to know that when it was presented in my materials class, and in your case, crystallography may prove to be very important. During our days as students, we simply are in no position to make informed judgments about what we will need to know and what we will not need to know. For that reason, you should strive to learn everything you possibly can, in order to be the best, most versatile, most complete engineer you possibly can when you graduate. So I say again, "study what interests you" and look forward to a great future.

Where to Study

It has come as a considerable surprise to me to see the number of students who want to leave their home country to study. Many express a desire to come to the USA, or to Europe, for study. Let me deal with undergraduate and graduate study separately.

For undergraduate study, I would strongly advise everyone to stay pretty close to home. It will usually cost less money, and it will be easier in the sense that the language, customs, and overall environment will be much more familiar. To travel to a foreign land as an undergraduate can be a pretty daunting experience, one that in too many cases results in isolation, difficulty fitting into the new environment, and educational failure. None of these are good outcomes, and most can be avoided by staying pretty close to home.

In terms of quality of education, it appears to me that the Indian Institutes of Technology (IITs) are all pretty good. I have never visited one of their campuses, but I have looked at a number of videos made by IIT faculty on various engineering topics. The material covered seems to be about typical of what I would expect to see in the US. I have three principal criticisms of the IIT engineering education:

(1) The material presented seems to me to be a bit dated, that is, old-fashioned. There is continued emphasis on graphical methods of solution, to the detriment of computer numerical solution techniques. This is unfortunate.

(2) The faculty leave me with the impression that most of them are simply scholars, but very few seem to be real, practicing engineers. This comes across in the choice of example problems, in their approach to problems, and their emphasis.

(3) The faculty are, quite naturally, almost entirely native Indian nationals. This is what we would expect. But since they are teaching in English (at least all the ones I have seen), their own limited ability in English is transferred to the students. The students really need better models, so that they hear and learn from their teachers more correct English. I will say more about this in another post.

Now there may be many of you who will be quick to disagree with me, and I cannot really argue with you. I certainly have a very small sample of Indian education, but I can only tell you what I think I see.

If you were to come to the US for undergraduate study, you might be surprised to find your situation not a whole lot better. In the US, many if not most of the undergraduate courses are taught, not by regular faculty, but by Teaching Assistants (TA s). These TA s are graduate students, many from India, the Middle East, Africa, China, and Japan. The choice of material and solution methods may be a bit more up to date, but none of these TA s is a practicing engineer, and they all have linguistic limitations as well.

In short then, I urge everyone to stay relatively close to home for undergraduate study. It just make sense, I think.

For graduate study, it is a different situation. By the time you are ready for graduate school, you should be (1) considerably more mature personally, (2) more confident in your own abilities, and (3) much more ready to deal with a new cultural environment. Some problems will remain, and may be major. If you go to Germany for example, but do not know German, there will be a major language difficulty (I could not study in Germany; I know only a few, very limited, phrases in German.) If you were to come to the USA, the language would be English which you already know to some extent, but it would probably be somewhat new even so. American English is different from British English in some subtle ways, and the spoken language may be difficult for you even though you can read it well.

Sadly, in most American universities, you will find a huge emphasis on modern research ideas, and relatively little emphasis on actual engineering practice. The faculty are judged and rewarded for their research and the money that their research brings in, so naturally, that is what they tend to emphasize to their students. The world does not need countless “research engineers.” It does need a large number of highly skilled, well educated practicing engineers. But this is not where the money is for the schools, so this is not what they do.

In American universities, essentially all graduate courses are taught by regular faculty, so you would encounter the best faculty the school has to offer. You could expect to hear proper American English in the classroom all the time. You would still encounter only a relative few faculty that are actual practicing engineers (this conflicts with “research” which is where the money is).

It appears to me that a great many students come to the US to study, particularly with the hope that a student visa can be turned into a permanent visa and perhaps even eventual citizenship. Do not do this! Plan to make your home, in the long term, in your native country. The US does not need more foreign born engineers; it has plenty of native born engineers. Conversely, most of your countries have a great need for excellent engineers, people who can contribute to the economic and social development of your country. The very best people to do that are the ones born there. You can do that far better than I could. If I were to go to India, for example, I might be able to help some, but not nearly as much as you can. I would not know the customs and the culture, the languages, or the history like you do. Whether you do graduate school at home or abroad, plan to return home for the long term. That is where you can do the most good for mankind.


To sum up then, I recommend undergraduate work near your home. Graduate work may continue there, or abroad, but your goal should be to return to your home to make your career there. Be sure to study the topic that really interests you, and pay little or no attention to employment or salary surveys. You only want one job, and it will be there for you if you are really well prepared.


For quite some time now, I have been looking for a book that just does not seem to exist anymore. The title and author are --

Title:          Secondary Resonance and Subharmonics in Torsional Vibrations
Author:      Per Draminsky

It was published in Denmark, around 1961, or so I am told. It seems that it was probably a monograph, a single extended article that filled an entire volume of a journal.

If anyone know where this can be found, I would much appreciate help with it. If I can borrow it from a source, that would be wonderful. If it cannot be borrowed, can I pay to have it scanned in and sent to me as a PDF? Is there yet some other way?

I am hoping that, with the world-wide readership of ME Forums, someone will help me find this book. If you have some information, please send me an e-mail at


Thanks for your help.



Many thanks to Sunil Baily who pointed me in the correct direction. I now have, on my desk in front of me, the only library copy of this paper to be found in the Western Hemisphere. It was a bit of a struggle, but I finally got an Inter-Library Loan (ILL) through my local city library. This is going to be very interesting reading (I've already skimmed through it once lightly).


    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 19
    © Machinery Dynamics Research, 2015

Vibrations -- Part VI
Machinery Torsional Vibrations



    The preceding five parts of this series on vibrations have dealt with relatively simple system, even though those systems are representative of many real situations encountered in engineering practice. For this section, a very specific class of machinery vibration problems, the torsional vibration of engine-driven machine trains involving multiple degrees of freedom, is considered in more detail.
    The system considered here is one from the writer's own engineering experience, a small diesel powered generator set. The engine is a Detroit Diesel 2-71 engine driving a Lima Electric 20 KW generator to create 60 Hz AC power for a portable field electrical source. The system for torsional vibration analysis is shown schematically in Fig. 1.




    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 18
    © Machinery Dynamics Research, 2015

Vibrations -- Part V
Free-Free Systems


    In the first three parts of this series on vibrations, only single degree of freedom systems were considered. In Part IV of the series, the idea of multiple degrees of freedom vibrations was introduced particularly in the context of two degree of freedom systems. In this, the penultimate part of this series, another aspect of multidegree of freedom systems is introduced. This is particularly relevant to machinery vibration problems.

    Figure 1  Free-Free Translating System
    Consider the system shown in Figure 1. At first glance, it is very similar to the system considered in Part IV, but notice that there is only one spring here. The really critical distinction is that there is no part of the system that is stationary, nothing is anchored. Since both ends are free to move, it is called a Free-Free System.



1. Team building is very popular in industry these days, so here is a team building joke.

A group of mathematicians are attending a weekend seminar on team building. During the night, a fire breaks out in the room of one of the mathematicians. He quickly tears pages out of his notes and lights them on fire, one by one. He then runs down the hall, shoving burning sheets of paper under the doors of all the other mathematicians.

In the morning, after the building is burnt to the ground, the fire marshal asks how the fire spread so fast. The initiator spoke up and said, "I thought distributing the problem would lead to a quicker solution."

2. Summary of the important laws that MEs must know:

From statics,  Stuff does not move on its own.

From dynamics: Stuff fights back (Newton's 3rd Law)

From mechanics of materials: Stuff stretches and breaks (Hooke's Law)

1st Law of Thermo: You can't win.

2nd Law of Thermo: You can't break even.

3rd Law of Thermo: You can't stop playing.

Addendum: Entropy isn't what it used to be.

3. An engineer, a physicist, and a statistician go hunting together. When some game is sighted, the physicist calculates his trajectory using ballistic equations, but omits air resistance. His shot falls 5 meters short. The engineer adds a fudge factor to compensate for air resistance, but his shot fall 5 meters long. The statistician shouts, "We got 'em!"

4. An engineer and a physicist are lost in a hot air balloon drifting along. The physicist is busy trying to use sextant to determine their position when the engineer spots someone on the ground. The engineer yells, "Where are we?" The man on the ground calls back, "You are in a hot air balloon, 100 ft above ground." The engineer and the physicist look at each other and one says, "That man is a mathematician. His answer was entirely correct and completely useless."

5. There is a calculus party and all the functions have been invited. ln(x) is talking with some trig functions when he see his friend e^x sulking in a corner. He says, "What's wrong, e^x?" e^x replies, "I'm lonely," to which ln(x) replies, "You should try to integrate yourself into the crowd." In despair, e^x cries out, "It won't make any difference at all!"

6. If you can just remember all these jokes, you will be a hit at the next of those parties you imagine yourself being invited to.





A Community Built on False Values

This may well prove to be the least popular thing I ever post on this blog because what I have to say may offend many. I do not say it with the intent to offend, but because I am compelled to give a warning.

One of the most interesting things that has developed from my blog, Mechanics Corner, here on the ME Forum has been the opportunity to correspond directly with a modest number of readers. This has included both young men and young women scattered across India, Southeast Asia, the Middle East, and the rest the world. The majority of them are still students, still studying to become mechanical engineers. I have been somewhat amazed at the number of them that talk about (1) their strong intention to go on to graduate studies, and (2) their desire and intention to publish research while still in school, in some cases even below the baccalaureate level. I do not wish to discourage people from graduate study nor do I wish to dissuade them from publishing their work, but both of these strike me as somewhat inappropriate for an undergraduate engineering student. It appears to me that many are caught up in the ethos of academia which is misleading them with respect to what is really of value as preparation for an engineering career. Let me elaborate.

Let us begin by considering two words, science and engineering. Wikipedia tells us that science means knowledge, coming from the Latin root word scientia. The same source also tells us that engineering, which is derived from the Latin root ingenium, means "cleverness," and the second root word ingeniare, meaning "to contrive or devise." These definitions point to the fundamental distinction between science and engineering. The scientists, particularly the physicist, seeks to know, particularly to find new knowledge. The engineer, on the other hand, seeks to apply existing knowledge to the solution of problems of interest to society. It is evident that these two fields are very close to each other. We cannot be clever and inventive without knowing what has been known for ages. But engineering is about the application of knowledge, while science is about the search for knowledge.

Academia has lost its way. This is certainly true in the USA, in Europe, and it appears to be true in the rest of the world as well. Where the college or university once saw its role as preserving and passing along the best of human knowledge, to prepare people for a productive life, the schools have since become big businesses, focus on their influence, their endowments, and their prestige. In the past, faculty were valued for their knowledge and their ability to teach, that is, to pass along knowledge to those who studied with them. Today this has changed. Faculty are now valued for what they contribute to the image of the institution, for their reputations, for their publications which reflect favorably on the institution, and usually most of all, for the grants and other funding that they bring to the institution. (Notice that there is nothing about teaching in the present day evaluation of faculty; this is sad but it is absolutely true.)

In order for a faculty member to advance today, he must be interested in and doing those things which are seen as contributing to the image of the institution. Foremost for faculty, this means grant writing, research, and publication. It explicitly excludes professional engineering practice. Thus, the vast majority of engineering faculty today have little or no experience as practicing engineers. They have a lot of experience in obtaining funding, in writing papers, in giving presentations to prestigious audiences and other similar activities that will reflect favorably on their schools. But most have never solved an actual engineering problem from industry.

The reader may ask, "so how does this affect the students?" The answer is simple. The faculty talk about and praise their research, publications, and funding, and students are inclined to take these things as their own goals for the future. Thus if a student sees a faculty member advancing and doing well by publishing a lot of research (and no one ever evaluates the true value of most of that research), the student is inclined to assume that this should be their goal, their path to success as well. Nothing could be further from the truth for a baccalaureate or masters level engineer.

Most of us have heard the phrase "engineering research," and what these faculty members are doing is often described as "engineering research." But is this really engineering research as it is practiced in industry? Not at all. Over the years, I have worked in industrial "research organizations" of many sorts, but very, very little of the work done in those organizations is publishable for the simple reason that it is not fundamentally new. Engineering research, as practiced in industry, in most cases means going to the library to see if you can find a paper (or a book) where the problem you are currently dealing with has been previously solved, or at least a very similar problem that can serve as a model for you. If we talk about experimental engineering research, that usually implies experiments and measurements directed to answer very specific questions about the problem at hand, and almost never about fundamental physics or other "new" knowledge. Let me cite a few examples of engineering research that I have been involved with personally:

1. Many years ago, I conducted an experimental study of the flexural vibration of a sonar transducer head under a U.S. Navy contract. The transducer head is that part of the sonar device that comes in direct contact with the water in order to transmit, or receive, a sound wave. For analytical purposes, the sonar head is usually modeled as a rigid body, but it was generally understood that being a real, physical body with flexibility, there would be a degree of flexing involved as it moved rapidly back and forth. My research quantified the extent of that flexing and suggested the possible need for further stiffening of the design. There was no fundamentally new information; no new phenomenon were discovered, and there was nothing publishable other than a report to the U.S. Navy.

2. At one time, I was employed as a research engineer at the Homer Research Laboratories run by Bethlehem Steel Corporation, conducting research in cold rolling of steel strip. My particular assignment was to develop a mathematical model and a computer simulation based on that model for the multistand cold rolling mill. A significant part of my "research" was simply going to the library to search for work previously done by others about modeling the phenomenon that occur in the roll gap where the thickness reduction actually occurs. My "research" was largely the application of work done by numerous others, and it was not in the least bit publishable, although it was a valuable engineering tool for my employer.

3. I once worked for a company that assembled engine-generator packages, using both engines and generators made by others. My principal responsibility in that position was the torsional vibration analysis of these machines, essentially the forced response analysis of a rather complicated, multi-degree of freedom vibration system, done for every machine we shipped out. Even though this was after I had completed my college work, I had never studied systems quite like that before. So "engineering research" became a matter of learning about multidegree of freedom vibration analysis, becoming familiar with the modal method, learning about the Holzer calculation technique, and refreshing my memory about the application of Fourier series. Not a bit of this was new. Multidegree of freedom vibration goes back at least as far as the Lord Rayleigh in the mid-19th century if not earlier, the Holzer calculation dates from the early 20th century, and Fourier series date from the early 19th century. So, while there was nothing new in any of this, it was necessary "engineering research" in order to give me the capability to perform my assigned tasks.

4. While at the engine-generator company, I was asked to create a mathematical model and numerical dynamic simulation for a complex system consisting of a diesel engine with the governor, a generator with its exciter, and induction motor, and a pump. This system is the emergency core cooling system for a nuclear power plant. In the event of the loss of regular coolant flow to the core, the standby diesel engine is started and the speed stabilized by the governor. After this is done, the exciter is activated to apply the field to the generator windings, and power is delivered to the induction motor. This step again requires stabilizing the speed by the governor. The induction motor is rigidly coupled to the pump which provides water to cool the core. All of these steps must happen very quickly, typically in about 15 seconds, so there is a lot going on. In my own engineering education, I had learned about basic circuit theory, but I never studied much about motors and generators. Thus my "engineering research" at this point included a lot of study of motor/generator theory, all information that had been known since the early 20th century. There was nothing about the eventual simulation that was publishable research, but it was a valuable engineering tool for my company.

The point of the four little stories above is simply that, in most cases of engineering practice, "engineering research" is simply a matter of finding existing knowledge so that it may be applied to a current problem of interest to the employer. Only in the most rare circumstances is it about the search for new knowledge, knowledge previously unknown to anyone. And yet it is this last, the search for new knowledge that is the focus of most academic research. With some exceptions, academic research is rarely relevant to the actual problems of industry today.

Let me also make a few comments about graduate education. Without going into the broad topic of the degradation of education at all levels, let it suffice to say that there are, broadly speaking, two categories of engineers. Let us call the first category the Project Engineer, almost always an individual with a baccalaureate degree in engineering. The second category, which we will call the Advanced Engineer, is usually a person with a Masters or doctoral degree in engineering, although baccalaureate degree holders are not entirely excluded.

The Project Engineer has broad responsibilities for many types of projects, including design, manufacturing considerations, obtaining materials, meeting delivery schedule requirements, and resolving difficulties as they arise. He relies heavily on codes and standards in his design work, often employing "rules of thumb" instead of rigorous calculation; this is how the vast majority of engineering gets done. The Project Engineer draws on his engineering education background for understanding, but rarely makes a calculation and relies heavily on engineering intuition to do his job.

The Advanced Engineer is one who has chosen to deepen his technical expertise, and enjoys dealing with more complicated problems, particularly in terms of mathematical analysis. The Advanced Engineer may, but often does not, have broad project responsibilities, but he is expected to be more rigorous in his work and to have a greater knowledge base.  He is often seen as a resource person for the Project Engineer.

Industry in every country needs large numbers of Project Engineers; this is where the jobs are for most engineering graduates. Industry in every country needs a far smaller number of Advanced Engineers because their role is largely support for the Project Engineers. At times, when there is a great industrial surge, such as the USA experienced during the space program, there is a somewhat increased need for Advanced Engineers, but there is always a greater need for Project Engineers. Even when times are good, when industry is hiring many engineers, too much education can often be a disadvantage for a job seeker. The employer, seeking a Project Engineer, will often say when considering a person with an advanced degree, "This person has more education than my position requires. This candidate is likely to become dissatisfied with the job after I invest in training him to do it. It is better to hire someone with less education who will remain with my company indefinitely." I have seen this happen, and I have been a victim of it myself. Thus I encourage all to think carefully about their goals and their potential employment prospects when considering whether to go to graduate school or not.

Let me tell one more personal experience to illustrate the difference between the Project Engineer and the Advanced Engineer.

5. Not quite 20 years ago, I was employed by a manufacturer of aerospace components. A dispute arose with the US Federal Aviation Authorities (FAA) regarding the design adequacy of a particular component in one of our products. The component was a push rod, bent into what is sometimes called a "dog-leg" configuration (a sort of Z-shape), and is operated in both tension and compression. The FAA inspector argued that the pushrod might fail by buckling, and our project engineer was unable to convince him otherwise. The problem came to me to justify our design.

Now buckling is an instability phenomenon, and I saw immediately that because of the bent configuration of the rod, there was no possibility of instability but only further bending, and hence no possibility of buckling. This argument, however, did not persuade the FAA inspector. My only option, therefore, was to calculate the deflections of the pushrod when operated in compression. This is not a simple calculation, and no one in my company knew how to do it. I turned to the classic book on elastic instability of structures by the great Ukrainian engineer Stephen Timoshenko where I found a similar, slightly simpler, problem that I could use as a model. Following Timosheno's work, I made the calculations to show that there simply was no buckling potential, and that further the very most elementary deflection calculations gave an almost identical result. The FAA inspector was unable to respond.

I mentioned this last personal experience in part to show (1) my role as the Advanced Engineer in support of the Project Engineer, (2) and also to show how, in this case, "engineering research" amounted largely to resorting to the literature for results almost 100 years old. Once again, it must be noted that this "research" produced no new results and was therefore not publishable, but it was worth a lot of money to my company.

Well, if students are being misled by academia about the nature of actual engineering, what can they do about it? The answer is simple to describe, even though it may be more difficult to put into practice. The short answer is, "Look for actual engineering experience for yourself outside of academia." How is this accomplished?

1. One of the classic ways to gain real experience has always been to look for work opportunities during the summer or other school vacation period in actual industry. Now it is obvious that working as a sacker in a grocery store will not provide much useful experience for someone who aspires to be come a machine design engineer. But work in a factory, on an assembly line, or even just distributing parts to an assembly line, will provide much useful insight into the nature of engineering work, the work environment, the demands, the expectations, and the hazards. If if you cannot get engineering work as an undergraduate, there is valuable experience to be gained simply by working around engineers.

2. In the USA, many engineering colleges provide a work/study program called Cooperative Education (Co-Op for short) in which a student, usually beginning in the second year, goes to school for one term and then goes to work in some actual industrial environment for the next term, alternating this pattern until graduation. Many students spend all their Co-Op work terms with the same company, but others will sample several different companies. If a student does well during his work experiences, this often leads to a job offer at the end of his college education. By that time, the student understands what is expected of engineers in that particular company, and the company has a understanding of the value of that student as a permanent employee. If Co-Op is available at your school I strongly urge you to take advantage of it.

3. Look for part-time work while in school with some actual, industrial firm, where you can see and perhaps participate in actual engineering work. This is an additional burden to your school work, but the opportunity to see the connection between school work and engineering practice can be invaluable. (I had a student once who worked in a battery factory while he was taking my Theory of Machines course. He was seeing, and working with on an everyday basis, many of the exact mechanisms that we were studying in class. He got an extraordinarily good education out of the combination.)

4. The SAE (the organization formerly known as the Society of Automotive Engineers but now legally simply SAE) organizes and conducts many student design competitions for engineering students. A number of these are structured around the design and construction and eventually racing various types of small race cars. Although done within the academic context, this provides students with a real engineering experience. If your school has such a competition, I strongly urge you to be a part of it. If your school does not have such, then I urge you to ask the school to get involved with the SAE student design competitions.

Let me close with one final story from my own experience, a story where I was simply an observer, not a participant at all. A company where I was employed hired two new graduate engineers, one from each of the two major engineering schools in my home state. One of the schools is known for being very practical and down to earth, while the other is known to be much more theoretical, more elegant, more research oriented. Each of these new employees was given a similar project to begin, the design of a small power transmission shaft. The graduate of the very down to earth engineering program got right to work, following steps he had learned in an undergraduate machine design class. He had an acceptable design in a matter of a few days. The graduate of the elegant, research oriented institution fumbled around for literally weeks, starting over time and again and essentially unsure how to proceed. He knew many of the things that needed to be considered, but he had no way to go about working through them systematically. It was very evident to me which one of these would make the better engineer.

I urge all students therefore to keep their eyes clearly fixed on the goal of engineering (assuming that really is their goal) and not let research, publication, and advanced studies cloud their vision.



    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 17
    © Machinery Dynamics Research, 2015


Vibrations -- Part IV
Multiple Degrees of Freedom


    The first three parts of this series have involved only a single mass moving in a single direction. Such a system constitutes a single degree of freedom. In this part, a second mass is added which changes the required approach considerably. The new system is shown in Figure 1.
    Fig. 1  Two Degree of Freedom System

    In the upper part of the figure, (a), the system is shown at equilibrium rest with no strain in either spring. In the lower figure, (b), the system is displaced x₁ and x₂ under the action of the applied external forces F₁(t) and F₂(t). The problem to be addressed in this part is the determination of the dynamic response of the system.



    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 16
    © Machinery Dynamics Research, 2015

Vibrations -- Part III
Effects of Damping


    In the previous discussions of the simple, displacement driven mechanical oscillator, damping has been explicitly omitted. In this part, viscous damping is taken into account. Viscous damping is the effect of forces that (1) always oppose existing relative motion, and (2) are proportional to the relative velocity between surfaces. It always removed energy from a system, converting mechanical energy into heat energy that is then lost by conduction, convection, or radiation. Note that, with no motion there is no viscous damping force. Viscous action is associated with surfaces separated by a film of oil, grease, or other viscous substance (such as animal fat, glycerin, or any other viscous fluid).
    There are many other types of energy dissipation mechanisms, including dry friction (Coulomb damping), aerodynamic drag (proportional to the square of velocity), and various other nonlinear damping mechanisms. In many cases, these other models are closer to reality, but there is a reason why the viscous damping is often the preferred modeling technique instead; it is mathematically tractable, which is to say, that it lends itself to mathematical solution far more readily than most other models. (Tractable is simply a big word, popular with mathematicians, meaning that something is easy to work with for a solution.) In this part of the series, the same system considered previous is again presented in slightly modified form; a viscous damper is added as shown in Figure 1.
    [Figure 1  Damped, Displacement Driven Mechanical Oscillator.]





    Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 15
    © Machinery Dynamics Research, 2015

Introduction & Review

    In Part I of this discussion, the single degree of freedom oscillator was introduced with displacement excitation. The system is shown in Figure 1.

    The impressed support motion is s(t) and the response of the mass is measured by x(t). As shown in the upper figure, s(0)=0, x(0)=0, and there is no strain in the spring. The elongation (or compression) of the spring is s(t)-x(t), so that the force acting to the right on the mass is F=K[s(t)-x(t)]. Applying Newton's Second Law gives the system equation of motion


    which may be re-written as


    ω_{n}²=K/M= square of the natural frequency of vibration. The quantity ω_{n} (or ω_{n}²) is a fundamental system property.
    The driving displacement was specified as


    and the solution was eventually determined, subject to the provision ω_{n}²≠Ω². In this part, the objective is to investigate what happens when the excitation is near or at the natural frequency, Ω≈ω_{n}. The frequency response plot, shown in Part I, leads us to think that the oscillations will be catastrophically large near resonance, but that is not the whole picture.




Mechanics Corner
    A Journal of Applied Mechanics and Mathematics by DrD, # 14
    © Machinery Dynamics Research, LLC, 2015

SDOF Vibrations -- Part I
Undamped System With
Non-Resonant Conditions



    The undamped single degree of freedom oscillator is a suitable model for countless physical systems. It might represent a wheel on a vehicle (without shock absorbers), a machine on an elastic foundation, a sensitive instrument mounted on a shaky support, or any number of other possible real situations. A simple schematic diagram for such a system is shown in Figure 1 below.

    [Figure 1  Undamped SDOF Oscillator with Base Excitation.]

    The impressed support motion is s(t) and the response of the mass is measured by x(t). As shown in the upper figure, s(0)=0, x(0)=0, and there is no strain in the spring.

SDOF Vibs1.pdf




    Mechanics Corner

    A Journal of Applied Mechanics and Mathematics by DrD, #13

    © Machinery Dynamics Research, LLC, 2015



Numerical Methods

Roots & Solutions of Equations




    When we write a mathematical expression of the form y=f(x), a value of x for which y=0 is called a root of the equation. The root is a value of x at which the ordinate is zero and the curve passes through the x-axis.

    Further, we are often called upon to consider two equations of the form y=f₁(x) and y=f₂(x), each of which defines a curve in the x-y plane. To find a solution for this system means to find a pair of numbers, (x,y), such that the point represented by that pair is simultaneously on both of the curves.

    Everyone who aspires to become an engineer learns in their pre-college mathematics about finding roots of linear and quadratic equations and about solving systems of linear simultaneous equations. We learn that finding roots of equations of first and second degree (linear and quadratic equations) is a fairly simple matter, but that roots of equations of higher degree is difficult to impossible, depending on the exact situation. We learn that solving a system of two simultaneous linear equations is a simple matter, a system of three simultaneous linear equations is still manageable, but more than three equations becomes very laborious. Systems of nonlinear equations are rarely dealt with at all at the introductory level.

    As has been demonstrated in previous articles on Kinematics and Statics by Virtual Work, these problems lead to some equations and systems of equations that are at times extremely difficult, or impossible, to solve by traditional algebraic methods. This points to the need for a numerical approach to the solution of these systems.




Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, #12

© Machinery Dynamics Research, LLC, 2015



Numerical Solution of

Ordinary Differential Equations




When we take the mathematics course titled Differential Equations, we learn a bag of tricks for the solution of many different types of differential equations. We also learn that every different type seems to require a completely new approach. There is no general approach to differential equations as a whole. This is rather disheartening news. We also learn that for linear ordinary differential equations, there are a number of fairly general methods, and hence much of our study tends to focus on systems described by this class of equations. But what are we to do when we need to understand systems not described by linear differential equations?

One of the earlier approaches that enjoyed some considerable success was electronic analog computation (there were also mechanical analog computers used earlier, such as the "ball and disk integrator" of the Norden bomb sight). In its electronic embodiment, analog computation involved the construction of a DC circuit that obeyed the same differential equation as the original system of interest. Imagine that we are interested in a spring--mass oscillator, subject to velocity squared damping. This system obeys the differential equation




Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, # 11

© Machinery Dynamics Research, LLC, 2015



Eksergian's Equation


Motion for SDOF






In undergraduate engineering education, when someone says "equation of motion," it is almost reflexive to think "Newton's Second Law of motion." Recall that Newton's Second Law says


F=m a


where both the left and right sides of the equation are vector expressions. Vector are very powerful, but they are also very demanding for proper handling. Energy quantities, which are scalars, are much easier to work with, by comparison. In most undergraduate work, and much graduate work as well, Newton's Second Law is the first, last, and only word to be said about equations of motion. But in fact, there is more, much more!

The most commonly discussed part of "more" is what is called the Lagrange equation of motion, an energy based approach to obtaining the equations of motion (as opposed to a vector approach) that originated with J.L. Lagrange (1736-1813). This approach has great applicability and will be discussed in detail in a later article.

A much less well known part of the "more" is what is called the Eksergian equation of motion, an energy based approach to the equation of motion for single degree of freedom systems. Since it only applies to SDOF systems, one might ask, "Why bother? Why not just use the Lagrange equations?" The answer is two fold: (1) the Eksergian approach is slightly easier than the Lagrange equation in application, and (2) the Eksergian approach offers more insight into the meaning of terms.

The Eksergian approach first appeared in print in English with Eksergian's 15 part paper titled "Dynamical Analysis of Machines," appearing over the years 1930 -- 1931, although there are hints that something similar may have appeared earlier in German. This series of papers was extracted from Eksergian's doctoral dissertation at Clark University, 1928. In many ways, Eksergian's work was ahead of its time; it is well suited to digital computation which was virtually nonexistent at the time that this work appeared, but it is too labor intensive for hand computation. This is probably why it is relatively obscure. Eksergian's equation is particularly useful for systems that are kinematically complicated.

 Eksergian's Equation of Motion for SDOF.pdf.467597bd8f63b9f0057f49487b2f4bac


An Integrity Problem


The article referenced below points to a serious integrity problem, one that should be a matter of concern to all engineers. Is their no honor among these people? Is this how India expects to advance? By fraud?

It involves blatant cheating on exams. Most of us do not enjoy taking exams, but we recognize that they are necessary to evaluate who is competent and who is not. The determination of who is competent to practice any profession, be it law, medicine, engineering, etc., is a matter of concern to all of society. It is damaging to society as a whole when those who are not competent, for whatever reason, are allowed to practice, putting society at risk of inferior work.

The Daily Mail article includes pictures showing friends and family members passing notes to those taking their final exams. The whole matter appears to be very poorly policed. Why is this possible? Why is not the exam site secured? It makes a joke out of the entire examination process, and renders it meaningless. This degrades the work of those who are diligent and work hard, right along with those who take the lazy way. Shame!!



The following is a verbal description of a Doonesbury cartoon of unknown date by Garry Trudeau. Doonesbury has long been one of America’s major cartoon strips, with a very dry wit and a decidedly left-of-center outlook. I found this today in going through some old files.

SCENE: A college classroom, the teacher lecturing in a rather absent minded fashion, the students silently bent over, taking notes and keeping their heads down.

TEACHER: Of course, in his deliberations on American capitalism, Hamilton could not have foreseen the awesome private fortunes that would be amassed at the expense of the common good.

TEACHER: Take the modern example of the inventor of the radar detector. In less than ten years, he made $175 million selling a device whose sole purpose is to help millions of people break the law.

TEACHER: In other words ...

STUDENT (suddenly sitting up and interjecting): Maybe the fuzz buster is a form of Libertarian civil disobedience, man. You know, like a blow for individual freedom.

TEACHER: I ... I don’t believe it!

STUDENT: Believe what, man?

TEACHER (smiling in happy elation!): A Response! I finally got a thinking response from one of you. And I thought you were all stenographers! I have a student! A student LIVES!

TEACHER (kneeling down, hand extended like one might approach a shy animal): Who are you lad? Where did you come from? Don’t be frightened ...

STUDENT: (looking around himself): What’s the deal here? Am I in trouble?

The above all appeared in print many years ago, but it is an apt description of Mechanics Corner.



Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, #10

© Machinery Dynamics Research, LLC, 2015



Virtual Work -- Part II (Revised)




The main ideas related to virtual displacements and virtual work were introduced in a previous article titled Virtual Work -- Part I; understanding of that article is essential background for this article.

Everything that is really necessary to be said about virtual work has been said previously; there is really no need to say anything more. Having read that, the reader is entitled to ask, "Then why are we spending time on a second article on the same topic?," an entirely valid question. The answer in a single word is convenience. While all that is necessary, that is essential, has been said, there remains more to be said that will make the ideas of virtual work more powerful and convenient to use. The purpose for this article is to bring to bear the idea of potential energy which forms a natural extension to virtual work.




Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, #9

© Machinery Dynamics Research, LLC, 2015



Virtual Work -- Part I




The whole topic of virtual work is one that is usually not well handled at the undergraduate level (and frequently not well done at the graduate level, either!). It is, however, a very powerful concept, and critical to the application of many of the most powerful tools available for both statics and dynamics.

The term virtual is an old word (preceding the current usage in computer related matters by several hundred years), meaning something proposed for consideration and discussion as opposed to something that actually happens. It is an adjective, and is used frequently to modify such nouns as displacement and work. Thus a virtual displacement is a possible displacement of the system under consideration, not an actual displacement of the system (the distinction is initially not easy to grasp, but it will become clear if you bear with it!). A virtual displacement is an infinitesimal displacement, of the most general sort possible consistent with the system constraints.

What does that mean? Consider a block sitting on a solid plane surface. The block can be moved parallel to the plane, so a virtual displacement must include any and all possible infinitesimal displacements parallel to the plane. On the other hand, the block cannot be moved downward through the plane; the solid surface is a constraint. Thus virtual displacements of the block do not included downward displacements.